How can I "normalize" the scale of what seems to be either an infinitely large or infinitely small object
Normalize dimensions.

Look at the dimensions in N panel and choose the largest eg for (1, 2, 3) is 3. Then scale by 1 / 3 = 0.3333 to make the largest dimension 1. If the dimension is (0, 0, 0) there's nothing can be done.

Script to do this, scales such that largest dimension of selected mesh objects is set to max_dim.  (Used 2 as default to correlate with cube sphere etc)

import bpy

max_dim = 2

context = bpy.context

mesh_obs = (o for o in context.selected_objects 
        if o.type == 'MESH' and o.dimensions.length)

for o in mesh_obs:
    o.scale *= max_dim / max(o.dimensions)